The video and solutions are very confusing. I lost points on this in actual exam, Watched it over 3 times still don’t get it! Is there a shortcut for this?? The long explanation is impossible to do during the actual exam.
Video solves an example (517!/24^x)
Why can’t 24 be 3x8 to solve this?
Why is 514 not the answer but 171?
How do we know what limiting factor is? How is number line helpful here?(shown in the video; THE MOST confusing part)
Need a short and simple explanation and shortcut for this that is easy to understand and apply?
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Because to count the number of 8’s you’d require counting the number of “triple copies” of 2 (how many groups of 3s you can make with the available amount of 2’s), so like why not just work with the number of 2’s from the get go. In general, you can imagine that it’s easier to deal with the prime factors for the same aforementioned reason.
Because there are 514 copies of 2 in the prime factorization of 517! from which you can make only \lfloor \frac{514}{3} \rfloor = 171 copies of 8. Needless to say, this is because you can only have 171 “full” groups (each group having 3 2’s) from the total 2’s available to you.
Well, if you’re confused then you can count the number of 8’s you can have and compare it with the number of 3’s there are in the prime factorization of 517!.
In your case, you can “make” 171 copies of 8, but have access to 256 copies of 3. Building off this, the “limiting factor” should be pretty evident.